Progestin Permeation through Polymer Membranes IV: Mechanism of Steroid Permeation and Functional Group Contributions to Diffusion through Hydrogel Films

For clinical studies, especially hioavailahility or hioequivalency studies, collect ion and analysis ot‘urine samples rather than plasma samples may he prel‘erahle (6).The distribution of chlorthalidone between plasma and erythrocytes is not instantaneous, so it is difficult to obtain a blood sample and to prepare the plasma quickly enough so that the determined chlorthalidone concentration is the same as the plasma concentration in rirw (7). The analysis of urinary samples can he accomplished rapidly with the fully automated system.

REFERENCES ( 1 ) M. M. Johnston, H. Li, and D.Mufson, J. Pharm. Sci., 66, 1735 ( I 9.77). ( 2 ) 1’. (’ollste, M. Garle, M. 1). Rawlins, and F. Sjoqvist, Eur. J. Clin. /’htJrnlfl(’fJ/..9, (1976). ( 3 ) H. L. J. Fleuren and ,J. M. van Rossum, J. Pharmacokinet. Hiepliarm., 5 , 359 (19771.

( 4 ) K. H. Reyer and J. R. Baer, Pharmacol. Rw.,13.517 (1961). ( 5 ) M. Rosenherg, H. Li, and M. M. Johnston, in “Aclvances in Automated Analysis, Technicon International Congress,” vol. 2, E. C. Barton, A. Conetta, M. cJ. F. I)u Cros, F. -1. Kabot, It. K. Love, C. Maddix, J. F. Murdock, and L. Perlman, Eds., Mediad, Tarrytown, N.Y., 1977, pi). 279-283. ( 6 ) W. Riess, U. C. Ihbach, I). Rurckhardt, W.‘I’heohald, P. Vuillard, and M. Zimmerli, E u r . J . Clin. Pharmacol., 12,375 (1977). (7) H. I,. J. M. Fleuren and J. M. van Rossum, J. Chromatogr., 152. 41 (1978).

ACKNOWLEDGMENTS Presented in part a t the 7th Technicon International Congress, December 1976, and a t the APhA Academy of Pharmaceutical Sciences, Phoenix meeting, November 1977. The authors thank Mr. M. Patel Ior excellent technical assistance.

Progestin Permeation through Polymer Membranes IV: Mechanism of Steroid Permeation and Functional Group Contributions to Diffusion through Hydrogel Films G. M. ZENTNER, J. R. CARDINALx, J. FEIJEN, and SUK-ZU SONG Itrceived September 7, 1978, from the Department o/ Pharmaceutics, College ( I / Pharmacy, Uniuersity of [ I t a h , Salt Lake C i t y , LU’ I:‘ Accepted for publication January 26, 1979.

X iI

Abstract 0 Hydrogel films were prepared from hydroxyethyl methacrylatc. hoth with (Film 11) and without (Film I) 5.25 mole % of ethylene glycol dimethacrylate. Permeation, diffusion, and partition coefficients I’or progesterone, testosterone, nandrolone, norethindrone, l7a-hyctroxyprogesterone. estradiol, and hydrocortisone were determined. A ~ h t permeation e model was proposed hased on the separation’of a domain (H) cornposed of “hulk-like” water and a domain (A) composed of polymer, interfacial water, and bound water present in the films. The separate contrihutions from the “pore” and “solution-diffusion” mechanisms to the total permeability were calculated from the model. Steroid permeabilities through Films I and I1 were analyzed in accordance with this model. Permeation of Film I1 occurred oia the solution-diffusion mechanism. Permeation of Film I occurred predominately by the pore mechanism with a small contrihntion (-20%) from the solution-diffusion inrchaniam. The latter contribution was dependent on the solubility of 1 he solute within the A domains ofthe hydrogel film. Functional group contritwtions to permeation of Film I1 were ascribed to either steric or hydrogen bonding effects. Keyphrases Progesterone-permeation through hydrogel films, models, structure-activity relationships, steroids 0 Hydrogel filmsprogesterone permeation, structure-activity relationships, steroids, models Structure-activity relationships-steroid permeation through hydrogel films Models-steroid permeation through hydrogel films

In previous reports from this laboratory (1,2), the permeation mechanisms of a model hydrophobic drug, progesterone, through poly(hydroxyalky1methacrylate) films were examined. The importance of film hydration was emphasized. Similar conclusions were drawn by others (3-5) for hydrophilic solute permeation through hydrogel films. Several investigators (2, 4, 5) indicated that, depending on the hydrogel composition, either a “pore” or a “solution-diffusion” mechanism may dominate permeation. For polymers prepared from various comonomers 970 / Journal of Pharmaceutical Sciences Vol. 68, No. 8, August 1979

or from hydroxyethyl methacrylate without added crosslinking agents, the pore mechanism dominates. A t high concentrations of the cross-linking agent, ethylene glycol dimethacrylate and possibly tetraethylene glycol dimethacrylate, the solution-diffusion mechanism appears to dominate permeation. These results were found for both hydrophobic (2) and hydrophilic (4,5) solutes. These conclusions are tenuous without further investigation. One problem is the partition coefficient reported for the hydrophobic solute progesterone (2). This value, which is >loo, appears to be inconsistent with a pore mechanism in which transport presumably occurs within water-filled pores or microchannels present in the film. For permeation within these channels, partition coefficients close to one are expected. Hydrophilic solutes in hydrogels generally exhibit partition coefficients close to this value (6). For this reason, the permeation mechanism of hydrophobic solutes through hydrogel films was examined in greater detail. The permeation characteristics for several steroids that have systematic structural differences were determined in films prepared from hydroxyethyl methacrylate, both with and without 5.25 mole % of ethylene glycol dimethacrylate as a cross-linking agent. The results substantiate previous conclusions concerning the two mechanisms for solute permeation in hydrogel films, provide an explanation for the proposed pore-type permeation mechanism for solutes having high hydrogelwater partition coefficients, and demonstrate the effects of steroid structural differences on permeation rates through hydrogel films. 0022-35491 791 0800-0970$0 1.OOlO

@ 1979, American Pharmaceutical Association

EXPERIMENTAL Materials-Hydroxyethyl methacrylate’ was a highly purified sample containing the following levels of impurities’: methacrylic acid, 0.06% ethylene glycol dimethacrylate, 0.024%; and diethylene glycol methacrylate, 0.24%. Ethylene glycol dimethacrylate2 was purified by base extraction and distillation. Azobis(methy1isobutyrate)was prepared by the method of Mortimer (7). Hydrocortisone3, 17a-hydroxyprogesterone?, progesterone3, testosterone?, nandrolone’, estradio13, n~rethindrone~, 6,7-3H-estradiols, and 1,2-:’H-progesterone6were used as received. TLC analysis, with 20% (v/v) ethyl acetate in toluene and 5%(v/v) methanol in chloroform as developing reagents, indicated that all steroids were pure. In all cases, a single UV-detectable spot was observed. Radiolabeled steroids had the same R/ values as the unlabeled counterparts, with >95% of the detectable activity associated with the primary spot. The remaining radioactivity was distributed evenly throughout the remainder of the plate. Methods- Hydrogel films were prepared by polymerization between sealed polyethylene plates a t 60° for 24 hr. Azobis(methy1isobutyrate) (7.84 mmoles/liter of monomer) was the initiator. Film I was prepared from a mixture of hydroxyethyl methacrylate and 40% (v/v) deionized water. Film I1 was prepared from a mixture of hydroxyethyl methacrylate with 5.25 mole % ethylene glycol dimethacrylate as the cross-linking agent and 40% (v/v) ethanol as the solvent. These mixtures were homogeneous before and after polymerization. Subsequent to polymerization, the films were soaked in water (changed repeatedly) f’or 3-4 weeks prior to use. The diffusion experiments were performed a t room temperature (24 f lo) in an all-glass cell described previously (1). An aqueous solution of 17n-hydroxyprogesterone,progesterone, testosterone, nandrolone, norethindrone, estradiol (-5 pg/ml), or hydrocortisone (-250 rglml) was placed into one chamber. The second chamber was filled with deionized water. The concentration increase was followed in the initially steroid-free chamber by UV spectrophotometry? or by liquid scintillation counting of‘the radiolabeled compounds using scintillation fluids and a scintillation counter9. Partition coefficients, defined as the ratio of the concentrations in the film and in the bulk aqueous phase, were determined by a solution depletion technique (1)in which 50 ml of a steroid solution was allowed to equilibrate with a known volume of polymer. Adsorption of the steroids onto glass was checked and was not a problem. The steroid equilibrium concentration in the hulk aqueous solutions was obtained as described previously. Film thicknesses ( 4 . 0 3 cm) were measured on the water-swollen films using a lightwave micrometer’0.

I l l 1 I

I

I

I

RESULTS AND DISCUSSION Permeability and diffusion coefficients for steroids in hydrogel films were calculated using:

where:

C0 = initial drug concentration in Compartment I V = compartment volumes (176 ml) K d = partition coefficient V, = membrane volume Cs = concentration in Compartment II at the onset of steady state ( t ,Y.

)

C4 = concentration in Compartment I1 a t the time t,, A = membrane area (14.2 cm2) 1 = wet membrane thickness U = DKd D = diffusion coefficient t,, = any time during steady state

’ Courtesy of Hydron Laboratories, New Brunswick, N.d.

f Monomer Polymer Laboratories, Philadelphia, Pa. ,’Steraloids Inc., Pauling, N.Y.

Sigma Chemical Co,, St. Louis, Mo. Amersham Corp.. Arlington Heights, 111. New England Nuclear, Roston, Mass. 7 Cary model 15, Varian Instruments. Palo Alto, Calif. Formula 950-A, New England Nuclear, Hoston, Mass. Model 3385. Packard Instrument Co., Downers Grove, Ill. Van Kueren Co., Watertown, Mass. 4

Journai of Pharmaceutical Sciences I 971 Vol. 68.No. 8.August 1979

meation is necessary to determine the dominant mechanism in Film I. The following discussion concerns the development of a model for diffusion within hydrogels that will provide for the calculation of these separate contributions from the data in Table I. This model is based on the physical-chemical properties of hydrogels and, in particular, on the water distribution within these films. Macroscopically, hydrogel films are homogeneous single-phase systems having water and polymer as components. Microscopically, the polymer and water can be visualized as separate dispersed phases. Jhon and Andrade (12) hypothesized that water can exist in a t least three different environments within synthetic hydrogel films in a fashion analogous to that proposed (13)for biological membranes. These environments include hydration or bound water, interfacial water, and normal or "bulk-like" water. The bound water is strongly associated with the polymer, probably as water hydrating the hydrophilic polymer groups. Interfacial water is not well defined but may be associated with hydrophobic interactions between the polymer segments. Bulk-like water is similar to bulk water in aqueous solutions. Sung (14)defined the concentrations of these various water types within poly(hydroxyethy1 methacrylate) films, prepared with and without 1 mole Ti of ethylene glycol dimethacrylate. The amount of bulk-like water is highly dependent on the total hydrogel water content. Films cross-linked with ethylene glycol dimethacrylate have a lower percentage of hulk-like water than hydrogels prepared without cross-linker a t equal total water contents. Interpolation of Sung's data is possible with the assumption that the distribution of water into bound, interfacial, and hulk-like fractions is similar in a 1-mole 70ethylene glycol dimethacrylate cross-linked gel containing the same weight fraction of total water (nonequilibrium value) as a 5.25-mole % cross-linked gel that is equilihrated with water. The equilibrium weight fraction of water in Film I1 is 0.35. A 1-mole Gib cross-linked gel contains less than 5 volume Ti of bulk-like water at this weight fraction. From this value, it may t)e inferred that the volume percent of bulk-like water in Film 11 approaches zero. A value of 22.8 volume 5% of bulk-like water is obtained for hydrogel films prepared without cross-linker having a total water weight fraction of' 0.43 (Film

I).

- -

72 3 1- m d r- c @I

972 I Journal of Pharmaceutical Sciences Val. 68,No. 8, August 1979

c?

t- t -

m c- c

These results, together with other data (2-6) on solute permeation through hydrogel films, provide the basis for the model of solute permeation through these films. In this model, the hydrogel films prepared without cross-linker are composed of two domains, A and B. Domain A is composed of polymer segments that associate by hydrophobic interactions and are surrounded by hound and interfacial water. Domain B is bulk-like water and forms the fluctuating pores described previously (11). Increasing the mole percent of cross-linker increases the amount of A and reduces the amount id B. A hydrogel such as Film 11, having no bulk-like water, is assumed to be composed entirely of A-type domains. Although the relative amounts of Domains A and B change as the mole percent of cross-linker is changed, the inherent permeabilities of the domains are assumed to retnain constant. Therefore, the total permeability of a hydrogel film is i i summation of the individual permeabilities of Domains A and B and varies in accordance with the volume percent of bulk-like water present. Transport in the hydrogel A domains occurs through the bound and interfacial water, through the hydrophobic regions, o r through some cmnhination of these. Irrespective of the specific transport region, permeation in the A regions occurs hy the solution-diffusion mechanism as previously defined. The K d values for transport in the A regions vary widely. depending on the solute solubility characteristics. Transport in the B domains occurs by simple diffusion in bulk-like water. The K d values must be precisely one since the solute is simply partitioning from bulk water into hydrogel domains of bulk-like water. Film 11, having no bulk-like water, is a diffusion barrier composed exclusively of A-type domains. As postulated in the model, solute transport occurs only by the solution-diffusion mechanism in such a film. Several lines of evidence support this contention and are consistent for both hydrophobic and hydrophilic solutes: 1. I t is supported by the cited data, which indicate that films containing high cross-linker concentrations have little or no hulk-like water. 2. Past work has shown that both hydrophobic (2) and hydrophilic ( 4 , 5 ) solutes exhibit limiting values for the diffusion coefficient as the cross-linking agent concentration increases. This result is inconsistent with a pore mechanism since, if this mechanism is operative, the diffusion

Table 11-Model Analysis of Steroid Permeation Data

Partial Molar Volumeo, cmVmole 237.4 252.0 218.1 269.8 272.1 214.9 273.6

Steroid Testosterone Norethindrone Nandrolone Progesterone 17&~Hydroxyprogesterone Estradiol Hydrocortisone 0

Diffusion Coefficient in Water, Do X 106 cm2/sec 6.04 5.83 6.35 5.59 5.56 6.41 5.55

Diffusion Coefficient in Bulk-Like Water of Film I,

DB x 107 cm2/sec 7.20 7.29 5.67 6.43 7.22 7.49 2.11

In ( D A D O ) -2.13 -2.08 -2.42 -2.16

-2.04 -2.15 -3.27

DBPT 0.80 0.77 0.75 0.76 -..0.82 0.77 0.88

Calculated from group contributions, Ref. 24.

coefficients must decrease with increasing cross-linker content due to a reduction in the average pore size as a consequence of reduced polymer chain mobility. 3. Film I1 was nearly impermeable to hydrophilic solutes such as inositol and sucrose (6). Since sucrose is of approximately the same molecular weight as the steroids used in the present study, its diffusion coefficient should be similar to the steroids if the pore mechanism is operative in Film 11. 4. The conclusion that transport occurs by the solution-diffusion mechanism in Film I1 is consistent with the high partition coefficients obtained for the steroids used in the present study. 5. The disproportionately large decrease in the permeability coefficient of hydrocortisone, a relatively water-soluble steroid, in Film I1 compared with Film I, coupled with a lower partition coefficient in Film I1 than in Film 1, suggests a dependence on bulk water not seen with the more hydrophobic steroids yet consistent with the pattern exhibited by the sugars. Film 1contains 22.8% of bulk-like water making up the B domains; the remainder is designated as A-type domains. Based on the proposed model and using the data in Table I, it is possible to estimate the contribution of each domain to the total permeability. Total Film I permeability can he represented as a summation of the individual domain contributions: PT =

fa

+ PH

(Eq. 2)

where:

PT = total permeability in Film I = permeability coefficient in the A domains PB = permeability coefficient in the R domains PA

The P A value is obtained from the relation PA = ( @ A )Py,where P y is the permeability coefficient of the solute in Film I1 and @ A is the volume fraction of A-type domains in Film I. The $A value is given by @ A = 1 JJH, where @R is the volume fraction of bulk-like water present in Film I(0.228). Equation 2 may be rewritten as:

PT

- ( & A )Py,= Pn

(Eq. 3)

The calculated P,q values represent the total permeahility attributable to the pore mechanism in Film I. By definition, the partition coefficient in the B domains equals one. Therefore, PR quantitatively equals the diffusion coefficient, U R , using f R = K d l J R . These values are given in Table I1 along with the ratio U H I P T . which is the percent pore-type permeation in Film I. This ratio is approximately 0.77 for all of the steroids investigated except hydrocortisone, which is 0.88. This finding indicates that the pore contribution to transport in Film I is similar for the more hydrophobic steroids, with the relatively water-soluhle steroid hydrocortisone permeating uia pores to a greater extent. This result is consistent with the proposed model. The relatively high values of DRIPT for all steroids suggest that permeation through Film I is dominated by the pore mechanism, a result consistent with previous work (2). The high K d values with Film I are consistent with the model. Although permeation is dominated by the pore mechanism, Film I is composed primarily of A-type domains, which dominate the partitioning of hydrophobic solutes but make little contribution to permeability. An implicit assumption of the model is that the A domains are similar in Films I and 11. Were this strictly true, the partition coefficients, which are dominated by A-type domains, in Film I should be related to those in Film 11 according to the volume fraction of A-type domains present

in Film I (0.772). These values are given in Table I as the ratio K f i I K i . The estradiol value is in close agreement with the predicted value. However, for the other steroids, except hydrocortisone, this ratio is approximately 0.54. Thus, qualitative agreement with the predicted value is found, but the quantitative agreement is not good. This finding implies that differences exist between the A domains of Films I and 11. This conclusion is expected based on the high cross-linker content in Film 11. The corrections that must be made to overcome this deficiency in the model are not readily apparent. Sufficient data were available from previous work (2) to test the model in predicting progesterone permeation in gels containing intermediate concentrations of the cross-linking agent ethylene glycol dimethacrylate. From the data of Sung (141, the volume percent of bulk-like water in a film prepared from 0.75 mole % of cross-linker is approximately 0.15. Based on this value, the permeability coefficient for progesterone in thia cross-linked gel can be calculated from Eq. 3 by assuming that the total permeation arising from transport in the B regions is given by P,q = DDB; is defined by the ratio @ % / Q R , where +%is the volume fraction of bulk-like water in the cross-linked film. By using the values found in Tables I and I1 for P:! and DB, 0.15 for @i, 0.228 for @,q, and 0.85 for &A, the total permeability for a film containing 0.75 mole TOcross-linker is calculated to be 6.45 X lod7cm2/sec. This value is in good agreement with cm2/sec (2). the experimental value of 5.64 X A theoretical treatment of solute permeability in hydrated polymer films was developed by Yasuda et af.(15). This treatment examines solute diffusion as a function of the free volume of the water-polymer system and predicts a linear correlation for plots of In (DlDo) uersus the square of the cross-sectional solute radius; D is the diffusion coefficient in the polymer film and DOis the diffusion'coefficient in bulk water. All solutes should correlate with a single straight line for a given polymer film provided the free volumes accessible to the various solutes are equal or can be resolved into equivalent contributions. Wisniewski and Kim (6) examined the permeabilities of ions and various other hydrophilic solutes in Film I-type hydrogels. A plot of In (DIDO) uer.w.9 the square of the cross-sectional radius was linear, with partition coefficients approximately equivalent to the volume fraction of bulk-like water in the film. This information suggested (6) that these solutes are restricted to permeation through the free volume of bulk-like water that is located in the B-type domains proposed in the present study. The DR values obtained in the present study represent the diffusion coefficients of hydrophobic steroids in the bulk-like water and, therefore, should correlate with the previous data (6). The values of In (D,q/Do) are given in Table 11. The DOvalues were calculated by a literature method (16). Lacey and Cowsar (17) showed that the minimal cross-sectional area for steroids of the type investigated in the present study is about 36 A2. When using this value to determine the minimal cross-sectional radius, a value of -2.7 for In (DRIDO)is required for an exact correlation with the data of Wisniewski and Kim (6). The data given in Table I1 are, in general, somewhat more positive than this value. Thus, as with the comparison with the K d values in Films I and 11 discussed previously, the podel presented here f i t s the expected value qualitatively but not ) to quantitatively. T h e somewhat larger values of In ( D ~ l n ocompared the predicted value arise from DH values that are too large. This result indicates that the model predicts a contribution from pore-type permeation that is too large. This discrepancy probably arises from the assumption that A-type domains have similar permeation characteristics in Films I and 11. The A domains are probably more permeable in Film I due to a lower cross-link density, leading to increased values for @ A P ~ . Therefore, the observed deviations are in the right direction. Journal of Pharmaceutical Sciences I 973 Vol. 68. No. 8, August 1979

T a b l e 111-Functional

Group Contributions to Diffusivity Relative Relative Molec- Diffusular ivity Volume Factor

Functional Group Changes

0

0

Lk

Testosterone OH

1.09

0.78

Nandrolone

Norethindrone

1.16

0.63

Progesterone

17a-Hydroxyprogesterone

1.01

1.37

Progesterone

Hydrocortisone

1.01

1.59

Nandrolone OH

/OH

served with Film 11, a solution-diffusion-type hydrogel. Changes in permeability coefficients are even less, indicating the importance of solute partitioning in the overall film permeation characteristics. Specific effects of solute structure on the diffusion coefficients in Film I1 are demonstrated more clearly by the comparisons made in Table 111. In this table, relative diffusivity factors, defined as the ratio of diffusion coefficients for steroids that differ by one structural feature, have been calculated. From the results in this table, the following conclusions were obtained: 1. The addition of a C-19 angular methyl group decreases diffusivity by a small factor (0.78) due to steric hindrance (relative K d values are independent of cross-linker content). 2. The same effect is seen on the addition of a C-17 ethynyl group, where diffusivity decreases by a factor of 0.63. 3. The addition of hydroxyl groups increases diffusivity by rather substantial factors, as seen from Comparisons 3 4 in Table 111. However, the effect of the first hydroxyl group is proportionately greater than the second and third hydroxyl groups (Table 111, Comparisons 3 and 5). 4. Changing the A ring of the steroid nucleus from an alicyclic (nandrolone) to an aromatic (estradiol) ring produces a decrease in diffusivity tiy a factor of 0.35. This decrease nccurs in spite of the change from a keto to a hydroxy function a t the %position of the steroid nucleus, which should increase diffusivity (Table 111, Comparison 6). Th e outlined group contributions to diffusivity should be valuahle in predicting approximate diffusion coefficients for other steroids. For example, the diffusion coefficient of testosterone may be approximated as follows. Beginning with progesterone, the effect of removing the side chain a t C-17 may he approximated by a factor of 1/0.63 (i.e., the inverse ofthe effect noted for the addition of a C-17 ethynyl group to nandrolone) times a factor of 1.37 (the effect of the addition of a C-17 hydroxyl group to progesterone). The result of this calculation gives 2.42 X cm2/sec for the diffusion coefficient of testosterone in Film 11, a result that compares favorably with the experimental value of 2.70 X lo-$ cm2/ sec.

CONCLUSIONS

1.01

1.16

Testosterone

0.88

2.41

Estradiol

0.99

0.35

17a-H ydroxyprogesterone

Hydrocortisone

Progesterone '0

/a '

Nandrolone

qJJ

Effect of Steroid S t r u c t u r e o n Permeation t h r o u g h Hydrogel Films-Previous work (1, 2, 18-23) demonstrated that hydrogels are excellent candidates for use in controlled-release drug delivery systems. The major advantages of these polymers for this purpose are biocompatibility (24,25) and the potential for controlling permeation characteristics through modifications in the hydrogel composition. Several studies using hydrophobic (2) and hydrophilic (4,5,20,21) solutes indicated that permeability coefficients can he varied by more than an order of magnitude by changing either the cross-link density or the monomer composition. Several studies (6,26) demonstrated effects of molecular structure on solute permeation in films prepared without added cross-linker. Th e importance of the solute molecular volume on the permeation characteristics has been demonstrated. However, no studies have considered the effects of molecular structure on permeability in films containing high cross-linker concentrations. Studies on the permeation characteristics of these films are of interest since intermolecular interactions between the solute and polymer segments are expected to increase and should dominate the overall permeability of these films. For poly(dimethy1 siloxane), a film in which solutes permeate by the scilution--diffusion mechanism, small changes in steroidal structure can lead to variations in the diffusion Coefficients of more than two orders ( i f magnitude (17). These dramatic changes in the diffusion coefficients in the solution-diffusion-type poly(dimethy1 siloxane) films are not ob974 I Journal of Pharmaceutical Sciences Vol. 68, No. 8. August 1979

Steroid permeation in poly(hydroxyethy1 methacrylate) films is complex. However, to a first approximation, the total observed permeatlility can be separated into pore and solution-diffusion components I)y applying a model descrihing the polymer films in terms of domains. Such an analysis supports the contentions of Film I being a pore-type and Film I1 being a soluticin-diffusion-type barrier for both hydrophilic and hydrophobic solutes. As expected from the inherent nature of solution-diffusion permeation, structural alterations in steroidal solutes affect diffusion. Decreases in molecular volume and increases in hydrogen bonding capacity increase diffusivity. By quantifying these effects for specific functional groups, it is possible to predict diffusion Coefficients. APPENDIX When a linear concentration gradient exists within a barrier film, the instantaneous concentration gradient within the film may he expressed as: dC - c;- c;, ---(Eq. Al) I dl where Ci and C;, represent the surface concentrations of the diffusant in the membrane a t the donor ( I ) and receptcir (11) sides of the film and I represents the thickness of the film. Provided that the partition coefficient, K d , is independent of the solute concentration, this equation may he rewritten as: dC K d ( C 1 - CII) (Eq. A'L) dl 1 where CI and CIIare the donor and receptor phase concentrations, respectively. Th e flux of solute within the film can be described by Fick's first law as:

--- -

J = - D - =dC =D-

cc; - C;,) 1

dl

(Eq. A3)

which can he rewritten as:

J

DK 1

I1 1

= 2(CI - C,,) = - (C, - (',I)

where the permeability U = DKd.

(Eq. A4)

During steady state, the flux out of Compartment I equals the flux into Compartment 11, which also equals the flux within the film barrier. This may be expressed as:

(Eq.A5) and

where V is the compartment volume and A is the film area. Subtracting Eq.A6 from Eq. A5 and equating to Eq. A4 give: (Eq. A7) Equation A7 is valid only during steady-state flux. Under these conditions, the concentrations of solute in Compartments I and I1 are C1 and CZa t t , (onset of steady state) and C3 and C4 a t ts. (any time during steady state). When using these concentrations and times for the limits of integration, Eq. A7 gives:

Steady-state mass balance gives:

cov=c,v+c2v+c,v, cov = c3v + c4 v + c, v,

(Eq. A9) (Eq. A10)

where COis the initial concentration in the donor phase, C , is the solute concentration within the film, and V , is the film volume. The film concentration may be defined as:

Substitution of Q. A l l into Eqs. A9 and A10 and rearranging give:

c, = 2 v 4-Kdv, cov - CZV --KdC2vm) 2

(Eq. A12)

REFERENCES (1) G. M. Zentner, J. R. Cardinal, and S. W. Kim, J. Pharrn. Sci.,67, 1347 (1978). ( 2 ) Ibid., 67,1352 (1978). (3) H. Yasuda, C. E. Lamaze, and A. Peterlin, J. Polyrn. Sci., Part A-2, 9,1117 (1971). (4) R. Y. S. Chen, Polyrn. Preprints, 15 ( 2 ) . 387 (1974). ( 5 ) S. J. Wisniewski, D. E. Gregonis, S. W. Kim, and J. D. Andrade, in “Hydrogelsfor Medical and Related Applications,” J. D. Andrade, Ed., American Chemical Society Symposium Series 31, 1976,p. 80. (6) S. J. Wisniewski and S. W. Kim, “Abstracts of 25th Meeting of Academy of Pharmaceutical Sciences,” American Pharmaceutical Association, Washington, D.C., 1978. (7) G. A. Mortimer, J. Org. Chern., 30,1632 (1964). (8) G. M. Zentner, J. R. Cardinal, and D. E. Gregonis,J. Pharrn. Sei., 68,794 (1979). (9) G. L. Flynn, S. H. Yalkowsky, and T. J. Roseman, ibid., 63,479 (1974). (10) M. F. Refojo, J . Polym. Sci., Part A-1, 5, 3103 (1967). (11) H. Yasuda, C. E. Lamaze, and L. D. Ikenberry, Makromol Chern., 118,19 (1968). (12) M. S. Jhon and J. D. Andrade, J. Ririmed. Mater. Res., 7 , 509 (1973). (13) R, J. Scheuplein, Riophys. J., 6.1 (1966). (14) Y. K. Sung, Ph.D. thesis, University of Utah,Salt Lake City, Utah, 1978. (15) H. Yasuda, A. Peterlm, C. K. Colton, K. A. Smith, and E. W. Merrill, Makrornol. Chern., 126, 177 (1969). (16) C. R. Wilke and P. Chang, Am. Inst. Chern. Eng, I, 264 (1955). (17) R. E. Lacey and D. R. Cowsar, Adu. Exp. Med. Riol., 47, 117 (1974). (18) M. Tollar, M. Stol, and K.Kliment, J. Riomed. Mater. Res., 3, 305 (1969). (19) V. Majkus, F. Horakova, F. Vymola, and M. Stol, ibid., 3,443 (1969). (20) J. M. Anderson, T. Koinis, 1’.Nelson, M. Horst, and D. S. Love, in “Hydrogels for Medical and Related Applications,” J. D. Andrade, Ed., American Chemical Society Symposium Series 31, 1976, p. 167. (21) D. R. Cowsar, 0. R. Tarwater, and A. C. Tanquary, in ibid., p. 180. (22) J. Drobnik, P. Spacek, and 0.Wichterle, J. Riomed. Mater. Res., 8.45 (1974). (23) R. A. Abraham and S. H. Ronel, ibid.. 9,355 (1975). (24) J. D. Andrade, Med. Instrum., 1,110 (1973). (25) B. D. Ratner and A. S. Hoffman, in “Hydrogels for Medical and Related Applications,” J. D. Andrade, Ed., American Chemical Society Symposium Series 31,1976, p. 1. (26) K. H. Lee, J. G.Lee, M. S. Jhon, and T. Ree, J. Rioeng., 2.269 (1978). ~~~

and: c3

=

2v

+ Kdv, cov - c4v --Kdc4vm) 2

(Eq. A13)

Substituting Eqs. A12 and A13 into Eq. A8 and rearranging give:

In the limit where K d is small and to,, approaches zero, CZ also approaches zero and Eq. A14 may be written as: (Eq. A15) Equation A15 was developed (9) for the case of quasi-steady-state diffusion in a film, assuming that the amount of solute in the film is negligible.

ACKNOWLEDGMENTS Presented in part at the APhA Academy of Pharmaceutical Sciences, Hollywood, Fla., meeting, November 1978. Supported by NIH Grant HD-09791-03. The authors thank Dr. S. W. Kim, Dr. D. E. Gregonis, and Dr. J. D. Andrade for their contributions to this work.

Journal of Pharmaceutical Sciences 1 975 Vol. 68, No. 8, August 1979